What is laplacetransform sqrt(t/pi) ?

The answer to laplacetransform sqrt(t/pi) is 1/(2s^{3/2)}

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laplacetransform sqrt(t/pi)

laplace transform

\frac{t}{π}

\frac{1}{2 s ^{\frac{3}{2}}}

Solution steps

L {\frac{t}{π}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{1}{π} L {t}

L {t} : \frac{π}{2 s ^{\frac{3}{2}}}

= \frac{1}{π} \frac{π}{2 s ^{\frac{3}{2}}}

Refine

\frac{1}{π} \frac{π}{2 s ^{\frac{3}{2}}} : \frac{1}{2 s ^{\frac{3}{2}}}

= \frac{1}{2 s ^{\frac{3}{2}}}

What is laplacetransform sqrt(t/pi) ?
The answer to laplacetransform sqrt(t/pi) is 1/(2s^{3/2)}